Semiconductor
quantum heterostructures
from band diagrams
to real-world applications
Lecture 5
Emmanouil Dimakis
contact: Institute of Ion Beam Physics and Materials Research
Helmholtz-Zentrum Dresden-Rossendorf (HZDR)
Tel: 0351 260 2765
email: [email protected]
web: http://www.hzdr.de
reading
III-V
IV
II-VI
semiconductor crystals
cubic semiconductor crystals
GaAs (Zincblende)
Si (diamond)
Si: 1s2 2s2 2p6 3s2 3p2
hexagonal semiconductor crystals
c
α
GaN (Wurtzite)
why 3C and not 2H? (polytypism)
stacking sequence along <111> :
ABCABC (3C) for zincblende (diamond) - cubic
ABAB (2H) for wurtzite - hexagonal
structural stability map
semiconductor alloys
random alloy
A0.5B0.5
A
B
semiconductor alloys
ordered alloy
A0.5B0.5
A
B
semiconductor alloys
phase separated alloy
A0.5B0.5
A
B
semiconductor alloys: lattice parameters
bandgap engineering (from UV to IR)
semiconductor alloys: energy bandgap
𝐸𝑔(𝐴𝑥 𝐵1−𝑥 𝐶) = 𝑥𝐸𝑔(𝐴𝐶) + 1 − 𝑥 𝐸𝑔
𝐵𝐶
− 𝑏(𝐴𝐵𝐶) 𝑥(1 − 𝑥)
𝐸𝑔(𝐴𝑥𝐵𝑦 𝐶1−𝑥−𝑦 𝐷) = 𝑥𝐸𝑔(𝐴𝐷) + 𝑦𝐸𝑔(𝐵𝐷) + 1 − 𝑥 − 𝑦 𝐸𝑔 𝐶𝐷
−𝑏 𝐴𝐵𝐷 𝑥𝑦 − 𝑏 𝐴𝐶𝐷 𝑥(1 − 𝑥 − 𝑦) − 𝑏 𝐵𝐶𝐷 𝑦(1 − 𝑥 − 𝑦)
𝐸𝑔(𝐴𝑥 𝐵1−𝑥 𝐶𝑦 𝐷1−𝑦) =
𝑥 1 − 𝑥 [𝑦𝐸𝑔
𝐴𝐵𝐶
𝑥 + 1 − 𝑦 𝐸𝑔
𝑥 ] + 𝑦 1 − 𝑦 [𝑥𝐸𝑔
𝑥 1 − 𝑥 + 𝑦(1 − 𝑦)
𝐴𝐵𝐷
𝐴𝐶𝐷
𝑦 + (1 − 𝑥)𝐸𝑔
𝐵𝐶𝐷
𝑦
direct bandgap for optoelectronics
direct-to-indirect bandgap transition
band offsets in heterostructures
3 different types of heterostructures